QNet Approximator
Website and Software Package, August 2009.
I directed the software development portion of a three-year NSF funded project to develop effective means to compute average cost bounds for stochastic queueing network control problems. Fourteen different undergraduate students with backgrounds in mathematics and computer science worked on the project, four of whom directly contributed to this software.
Fluid analysis of an input control problem
(publication link)
M. H. Veatch and J. R. Senning, Queueing Systems,
61(2), 87-112, 2009.
Abstract: A two-station network with controllable inputs and sequencing control, proposed by Wein (Oper. Res. 38:1065–1078, 1990), is analyzed. A control is sought to minimize holding cost subject to a throughput constraint. In a Lagrangian formulation, input vanishes in the fluid limit. Several alternative fluid models, including workload formulations, are analyzed to develop a heuristic policy for the stochastic network. Both the fluid heuristic and Wein’s diffusion solution are compared with the optimal policy by solving the dynamic program. Examples with up to six customer classes, using Poisson arrival and service processes, are presented. The fluid heuristic does well at sequencing control but the diffusion gives additional, and better, information on input control. The fluid analysis, in particular whether the fluid priorities are greedy, aids in determining whether the fluid heuristic contains useful information.
Beowulf Cluster Performance for a Dynamic
Programming Solution of a Two-Class Queueing Network
Unpublished manuscript, March 14, 2009.
Abstract: We describe an experiment designed to determine if a dedicated parallel cluster is effective in solving certain queueing network problems using dynamic programming. We show that the same domain decomposition method that is commonly used for solving elliptic partial differential equations with finite differences is effective for this class of problems and yields roughly the same parallel efficiency. Finally, we suggest that a modest program of research in high performance computing at Gordon College is both desirable and achievable.
Vedic Mathematics: Magical
Methods for Mathematical Manipulation?
Gordon College Faculty Forum, February 11, 2009.
Abstract: Published in 1965, the book "Vedic Mathematics" purported to explain a holistic system of mathematics that was found in the Vedas, some of the most ancient and sacred Hindu scriptures. Proponents claim that Vedic Mathematics simplifies many basic tasks, allowing seemingly difficult computations to be done mentally while critics believe that Vedic Mathematics is nothing more than another "fast math" system and is not derived from the Vedas at all. In my rather non-technical presentation, I'll demonstrate some Vedic computations, explain how and why some of them work, then explore some of the religious and political intrigue that surrounds this subject in India.
Homogeneous
Coordinates: They work, but where do they come from?
AMS-MAA Joint Mathematics Meetings, January 2008.
During the MAA session on Innovative and Effective Ideas in Teaching Linear Algebra I presented a talk on homogeneous coordinates that is appropriate for students in an introductory linear algebra course after they've seen bases and coordinate vectors.
Also available in PDF or OpenOffice.org Impress format.